A) \[2\]
B) \[4\]
C) \[6\]
D) \[8\]
Correct Answer: D
Solution :
\[\mathbf{a}+t\mathbf{b}\bot \mathbf{c}\] \[\Rightarrow \] \[(\mathbf{a}+t\mathbf{b})\cdot \mathbf{c}=0\] \[\Rightarrow \] \[\mathbf{a}\cdot \mathbf{c}+t\mathbf{b}\cdot \mathbf{c}=0\] \[\Rightarrow \] \[t=-\frac{\mathbf{a}\cdot \mathbf{c}}{\mathbf{b}\cdot \mathbf{c}}\] \[\Rightarrow \] \[t=\frac{(2\mathbf{i}+2\mathbf{j}+3\mathbf{k})\cdot (3\mathbf{i}+\mathbf{j})}{(-\mathbf{i}+2\mathbf{j}+\mathbf{k})\cdot (3\mathbf{i}+\mathbf{j})}\] \[\Rightarrow \] \[t=\frac{6+2+0}{-3+2+0}=8\]
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